{"paper":{"title":"On the non-periodic stable Auslander--Reiten Heller component for the Kronecker algebra over a complete discrete valuation ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kengo Miyamoto","submitted_at":"2016-01-23T09:13:28Z","abstract_excerpt":"We consider the Kronecker algebra $A=\\mathcal{O}[X, Y]/(X^2, Y^2)$, where $\\mathcal{O}$ is a complete discrete valuation ring. Since $A \\otimes\\kappa$ is a special biserial algebra, where $\\kappa$ is the residue field of $\\mathcal{O}$, one can compute a complete list of indecomposable $A\\otimes\\kappa$-modules. For each indecomposable $A\\otimes\\kappa$-module, we obtain a special kind of $A$-lattices called \"Heller lattices\". In this paper, we determine the non-periodic component of a variant of the stable Auslander--Reiten quiver for the category of $A$-lattices that contains \"Heller lattices\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06256","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}